How to find the factorial of a number using Recursion in JavaScript

October 7th, 2022 | 5 mins read

#javascript

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The factorial of a number, in mathematics, is written as n! which reads "n factorial". This factorial means n multiplied by every number that precedes it until 1.

So, 5! means 5 * 4 * 3 * 2 * 1 which is equal to 120.

There are many ways you can do factorials in JavaScript. In this example, we'll look at a recursion approach.

What is Recursion

Recursion is a concept in programming where a function calls itself and keeps calling itself until something stops it from doing so. If nothing stops it, an infinite recursion occurs which crashes your application.

Here's an example of recursion in JavaScript:

function printHello() {
  console.log("hello")

  printHello()
}

printHello()

As you can see, the printHello function calls itself. When printHello is called after the function definition, the console.log("hello") line runs, followed by the printHello() call. When printHello() runs, the console.log("hello") line runs again, followed by another printHello().

That's recursion happening. To avoid infinite recursion, we can apply a base case condition like this:

let counter = 0

function printHello() {
  console.log("hello")
  counter++

  if (counter > 6) {
    return
  }

  printHello()
}

printHello()

With this condition, when the counter becomes 7, the base case is met, the return statement is executed, and the recursion ends.

Let more about recursion with more examples in this video: Recursion in JavaScript (video)

Implement factorial with Recursion

To achieve this, let's start by creating a function that takes an n argument and multiples it by the number before n, that is, n - 1:

function factorial(n) {
  const preceding = n - 1
  
  return n * preceding
}

Then, the recursion:

function factorial(n) {
  const preceding = n - 1

  return n * factorial(preceding)
}

factorial(5)

What happens here is that when factorial is called with the argument 5:

  • the preceding variable becomes 4 (5 - 1)
  • then we execute n * factorial(4) which will not complete instantly because factorial(4) is a recursion

With factorial(4):

  • the preceding variable becomes 3 (4 - 1)
  • then we execute n * factorial(3) which will not also complete instantly because factorial(3) is a recursion

This keeps happening infinitely even when n becomes -1, -2 until the app crashes. So here, we need a base that lets the function know when to stop.

As I mentioned at the beginning, the factorial of a number is the number multiplied by its precedents until the number 1. So, we can create a base case that lets the factorial function stop recursing when n is 1 like this:

function factorial(n) {
  if (n === 1) {
    return n
  }

  const preceding = n - 1

  return n * factorial(preceding)
}

factorial(5)
// 120

Starting again, let's see how this recursion works.

factorial(5):

  • 5 is not equal to 1, so the base case isn't met
  • preceding is 4
  • return n * factorial(4) doesn't complete instantly as n (which is 5) needs to wait for factorial(4) to return something

factorial(4):

  • base case not met again
  • preceding is 3
  • return n * factorial(3) doesn't complete instantly as 4 needs to wait for factorial(3) to return something

factorial(3):

  • base case not met again
  • preceding is 2
  • return n * factorial(2) doesn't complete instantly as 3 needs to wait for factorial(2) to complete

factorial(2):

  • base case not met again
  • preceding is 1
  • return n * factorial(1) doesn't complete instantly as 2 needs to wait for factorial(1) to complete

factorial(1):

  • the base case is met as n (which is 1) is equal to 1
  • then we return n which means returning 1 from this function

Now, factorial(2) can complete its execution, which means n * factorial(preceding) becomes 2 * factorial(1) which becomes 2 * 1 which is 2.

2 is returned from factorial(2), so since this is completed, factorial(3) can also complete its execution. This means n * factorial(preceding) becomes 3 * factorial(2) which becomes 3 * 2 which is 6.

6 is returned from factorial(3), so since this is completed, factorial(4) can also complete its execution. This means n * factorial(preceding) becomes 4 * factorial(3) which becomes 4 * 6 which is 24.

24 is returned from factorial(4), so since this is completed, factorial(5), the first call, can also complete its execution. This means n * factorial(preceding) becomes 5 * factorial(4) which becomes 5 * 24 which is 120.

And 120 is returned from factorial(5) which is the result we were looking for.

So you see how the function keeps calling itself with different arguments are different points until a base case is met that stops the recursion.

Wrap up

As stated earlier, there are multiple ways to implement factorials in JavaScript. You can also use loops. But in this article, I've shown you how to use recursion.

I explained what Recursion is, and also explained the different steps that happen in recursion for our factorial function.

Check out this video to learn more about Recursion

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Articles written with by
Dillion Megida